Question: Solve for $x$ and $y$ using elimination. ${-4x+y = -8}$ ${3x-y = 5}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-4x+y = -8}\thinspace$ to find $y$ ${-4}{(3)}{ + y = -8}$ $-12+y = -8$ $-12{+12} + y = -8{+12}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {3x-y = 5}\thinspace$ and get the same answer for $y$ : ${3}{(3)}{ - y = 5}$ ${y = 4}$